The Reds are offering Mascherano a two-year extension and a pay rise in order to fend off interest from Barcelona.
The 25-year-old has two seasons left on his current contract with Liverpool, but has long been linked with a move to Barcelona.
The Sun says talks have begun over a new deal that would see Mascherano earn £5million-a-year and see him stay at Anfield until 2014.
